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Properties

Label 1145.2.a.f
Level $1145$
Weight $2$
Character orbit 1145.a
Self dual yes
Analytic conductor $9.143$
Analytic rank $0$
Dimension $22$
CM no
Inner twists $1$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [1145,2,Mod(1,1145)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1145, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("1145.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1145 = 5 \cdot 229 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1145.a (trivial)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: yes
Analytic conductor: \(9.14287103144\)
Analytic rank: \(0\)
Dimension: \(22\)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

$q$-expansion

The dimension is sufficiently large that we do not compute an algebraic \(q\)-expansion, but we have computed the trace expansion.

\(\operatorname{Tr}(f)(q) = \) \( 22 q + 7 q^{2} + 12 q^{3} + 27 q^{4} + 22 q^{5} + 2 q^{6} + 24 q^{7} + 18 q^{8} + 22 q^{9}+O(q^{10}) \) Copy content Toggle raw display
\(\operatorname{Tr}(f)(q) = \) \( 22 q + 7 q^{2} + 12 q^{3} + 27 q^{4} + 22 q^{5} + 2 q^{6} + 24 q^{7} + 18 q^{8} + 22 q^{9} + 7 q^{10} - q^{11} + 17 q^{12} + 17 q^{13} + q^{14} + 12 q^{15} + 29 q^{16} + 12 q^{17} + q^{18} + 25 q^{19} + 27 q^{20} + 3 q^{21} + 6 q^{22} + 13 q^{23} - 2 q^{24} + 22 q^{25} - 6 q^{26} + 30 q^{27} + 20 q^{28} - 8 q^{29} + 2 q^{30} + 35 q^{31} + 23 q^{32} - 9 q^{33} - 6 q^{34} + 24 q^{35} - 3 q^{36} + 11 q^{37} - 8 q^{38} - 2 q^{39} + 18 q^{40} - 4 q^{41} - 34 q^{42} + 34 q^{43} - 21 q^{44} + 22 q^{45} - 7 q^{46} + 27 q^{47} + 13 q^{48} + 32 q^{49} + 7 q^{50} - 9 q^{51} + 16 q^{52} + 15 q^{53} - 24 q^{54} - q^{55} - 31 q^{56} + q^{57} - 6 q^{58} - 21 q^{59} + 17 q^{60} + 26 q^{61} + 9 q^{62} + 52 q^{63} + 14 q^{64} + 17 q^{65} - 28 q^{66} + 22 q^{67} + q^{68} + 11 q^{69} + q^{70} - 6 q^{71} - 34 q^{72} + 23 q^{73} - 9 q^{74} + 12 q^{75} + 11 q^{76} - 22 q^{77} + 7 q^{78} + 50 q^{79} + 29 q^{80} + 6 q^{81} - 16 q^{82} + 39 q^{83} + 9 q^{84} + 12 q^{85} - 60 q^{86} + 14 q^{87} + 40 q^{88} - 15 q^{89} + q^{90} + 18 q^{91} - 18 q^{92} - 13 q^{93} + 6 q^{94} + 25 q^{95} - 46 q^{96} + 3 q^{97} + 63 q^{98} - 20 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Display 100 coefficients 10 coefficients

Embeddings

For each embedding \(\iota_m\) of the coefficient field, the values \(\iota_m(a_n)\) are shown below.

For more information on an embedded modular form you can click on its label.

comment: embeddings in the coefficient field
 
gp: mfembed(f)
 
Label   \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
1.1 −2.58727 −0.359067 4.69396 1.00000 0.929001 2.55370 −6.96998 −2.87107 −2.58727
1.2 −2.46170 3.12331 4.05995 1.00000 −7.68864 1.97457 −5.07096 6.75507 −2.46170
1.3 −2.01778 2.07161 2.07144 1.00000 −4.18005 1.53010 −0.144150 1.29156 −2.01778
1.4 −1.99198 −0.829558 1.96800 1.00000 1.65247 −1.28492 0.0637526 −2.31183 −1.99198
1.5 −1.63823 −2.35654 0.683790 1.00000 3.86055 1.94323 2.15625 2.55329 −1.63823
1.6 −1.25740 0.0307357 −0.418936 1.00000 −0.0386472 −2.48027 3.04158 −2.99906 −1.25740
1.7 −0.829850 0.959770 −1.31135 1.00000 −0.796465 4.15804 2.74792 −2.07884 −0.829850
1.8 −0.779907 3.25170 −1.39175 1.00000 −2.53603 3.14303 2.64524 7.57358 −0.779907
1.9 −0.266014 2.19272 −1.92924 1.00000 −0.583293 0.270332 1.04523 1.80800 −0.266014
1.10 −0.0901637 −0.0104553 −1.99187 1.00000 0.000942686 0 −3.73992 0.359922 −2.99989 −0.0901637
1.11 0.0122831 −2.88243 −1.99985 1.00000 −0.0354050 4.86591 −0.0491304 5.30840 0.0122831
1.12 0.658768 2.60461 −1.56602 1.00000 1.71583 −1.49651 −2.34918 3.78399 0.658768
1.13 1.23557 1.48263 −0.473373 1.00000 1.83189 4.32459 −3.05602 −0.801805 1.23557
1.14 1.23777 −1.66688 −0.467919 1.00000 −2.06322 −0.834225 −3.05472 −0.221495 1.23777
1.15 1.37320 −1.93726 −0.114311 1.00000 −2.66025 3.68675 −2.90338 0.752959 1.37320
1.16 1.67285 2.88428 0.798435 1.00000 4.82498 3.33138 −2.01004 5.31909 1.67285
1.17 2.17089 0.688715 2.71277 1.00000 1.49513 3.52889 1.54735 −2.52567 2.17089
1.18 2.35309 2.49925 3.53704 1.00000 5.88096 −3.96906 3.61679 3.24625 2.35309
1.19 2.35569 2.56759 3.54928 1.00000 6.04846 −0.335456 3.64963 3.59253 2.35569
1.20 2.50499 −2.24534 4.27500 1.00000 −5.62456 −1.16936 5.69886 2.04154 2.50499
See all 22 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 1.22
Significant digits:
Format:

Atkin-Lehner signs

\( p \) Sign
\(5\) \(-1\)
\(229\) \(1\)

Inner twists

This newform does not admit any (nontrivial) inner twists.

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 1145.2.a.f ✓ 22
5.b even 2 1 5725.2.a.k 22
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
1145.2.a.f ✓ 22 1.a even 1 1 trivial
5725.2.a.k 22 5.b even 2 1

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator \( T_{2}^{22} - 7 T_{2}^{21} - 11 T_{2}^{20} + 176 T_{2}^{19} - 124 T_{2}^{18} - 1772 T_{2}^{17} + 2857 T_{2}^{16} + \cdots + 5 \) acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(1145))\). Copy content Toggle raw display